Question

factorise the question: (1-x^2)(1-y^2)+4xy

Answer 1

Hey Juhi !

Here is your solution :

= ( 1 - x^2 ) ( 1 - y^2 ) + 4xy

= 1 - y^2 - x^2 + x^2y^2 + 4xy

= 1 + x^2y^2 - x^2 - y^2 + 4xy

By splitting 4xy,

= 1 + x^2y^2 - x^2 - y^2 + 2xy + 2xy

By regrouping terms ,

= 1 + x^2y^2 + 2xy - x^2 - y^2 + 2xy

= ( 1 + x^2y^2 + 2xy ) - ( x^2 + y^2 - 2xy )

= [ ( 1 )^2 + ( xy )^2 + 2 × 1 × xy ] - ( x - y )^2

Using identity :

( a^2 + b^2 + 2ab ) = ( a + b )^2

= ( 1 + xy )^2 - ( x - y )^2

Using identity :

( a^2 - b^2 ) = ( a + b ) ( a - b ).

= ( 1 + xy + x - y ) ( 1 + xy - x + y ).

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Hope it helps !!

Answer 2

Here is your in this photo.